Inserted: 30 mar 2021
Last Updated: 4 apr 2021
30 pages, 3 figures
We prove the $\Gamma$-convergence of the renormalised Gaussian fractional $s$-perimeter to the Gaussian perimeter as $s\to 1^-$. Our definition of fractional perimeter comes from that of the fractional powers of Ornstein-Uhlenbeck operator given via Bochner subordination formula. As a typical feature of the Gaussian setting, the constant appearing in front of the $\Gamma$-limit does not depend on the dimension.
Keywords: Gamma-convergence, Fractional perimeters, Gaussian analysis